Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization

Parameterized quantum circuits (PQCs) have been widely used as a machine learning model to explore the potential of achieving quantum advantages for various tasks. However, training PQCs is notoriously challenging owing to the phenomenon of plateaus and/or the existence of (exponentially) many spurious local minima. To enhance trainability, in this work we propose an efficient parameter initialization strategy with theoretical guarantees. We prove that by reducing the initial domain of each parameter inversely proportional to the square root of circuit depth, the magnitude of the cost gradient decays at most polynomially with respect to qubit count and circuit depth. Our theoretical results are substantiated through numerical simulations of variational quantum eigensolver tasks. Moreover, we demonstrate that the reduced-domain initialization strategy can protect specific quantum neural networks from exponentially many spurious local minima. Our results highlight the significance of an appropriate parameter initialization strategy, offering insights to enhance the trainability and convergence of variational quantum algorithms.